NTA JEE Mains 23rd Jan 2026 Shift 1

The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is ___ .

Let f be a twice differentiable non-negative function such that $$(f(x))^{2}=25+\int_{0}^{x}\left((f(t))^{2}+(f'(t))^{2}\right)dt$$. Then the mean of $$f(\log_{e}{(1)}),f(\log_{e}{(2)}),.....,f(\log_{e}{(625)})$$ is equal to:

Let |A|=6, Where A is a $$3\times3$$ matrix. If $$|adj(3adj(A^{2}\cdot adj(2A)))|=2^{m}\cdot3^{n},m,n\epsilon N$$, then m+n is equal to:

From the first 100 natural numbers, two numbers first a and then b are selected randomly without replacement. If the probability that $$a-b \geq 10$$ is $$\frac{m}{n}$$, gcd (m, n) = l, then m + n is equal to______.

Let the area of the region bounded by the curve y= max $${\sin x, \cos x}$$, lines x = O, $$x=\frac{3\pi}{2}$$, and the x-axis be A. Then, A+$$A^{2}$$ is equal to_____.

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R)
Consider a ferromagnetic material :
Assertion (A) : The individual atoms in a ferromagnetic material possess a magnetic dipole moment and interact with one another in such a way that they spontaneously align themselves forming domains.
Reason (R): At high enough temperature, the domain structure of ferromagnetic material disintegrates. Thus, magnetization will disappear at high enough temperature known as Curie temperature.
In the light of the above statements, choose the correct answer from the options given below :

The following diagram shows a Zener diode as a voltage regulator. The Zener diode is rated at $$V_{z}=5V$$ and the desired current in load is 5 mA. The unregulated voltage source can supply upto 25 V. Considering the Zener diode can withstand four times of the load current, the value of resistor $$R_{s}$$ (shown in circuit) should be ____ Ω .

Two small balls with masses m and 2m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about A is :

The moment of inertia of a square loop made of four uniform solid cylinders, each having radius R and length L (R<L) about an axis passing through the mid points of opposite sides, is (Take the mass of the entire loop as M) :

In hydrogen atom spectrum, (R ➔ Rydberg's constant)
A. the maximum wavelength of the radiation of Lyman series is $$\frac{4}{3R}$$
B. the Balmer series lies in the visible region of the spectrum
C. the minimum wavelength of the radiation of Paschen series is $$\frac{9}{R}$$
D. the minimum wavelength of Lyman series is $$\frac{5}{4R}$$
Choose the correct answer from the options given below :